A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. comprising part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction.
In a manufacturing process using a lithographic projection apparatus, a pattern (e.g. in a mask) is imaged onto a substrate that is at least partially covered by a layer of radiation-sensitive material (resist). Prior to this imaging step, the substrate may undergo various procedures, such as priming, resist coating and a soft bake. After exposure, the substrate may be subjected to other procedures, such as a post-exposure bake (PEB), development, a hard bake and measurement/inspection of the imaged features. This array of procedures is used as a basis to pattern an individual layer of a device, e.g. an IC. Such a patterned layer may then undergo various processes such as etching, ion-implantation (doping), metallization, oxidation, chemo-mechanical polishing, etc., all intended to finish off an individual layer. If several layers are required, then the whole procedure, or a variant thereof, will have to be repeated for each new layer. Eventually, an array of devices will be present on the substrate (wafer).
The radiation system as well as the projection system of a lithographic apparatus generally comprise components to direct, shape or control a beam of radiation. Generally, the projection system comprises means to set the numerical aperture (commonly referred to as the “NA”) of the projection system. For example, an adjustable NA-diaphragm may be provided in a pupil of the projection system. The radiation system typically comprises adjusting means to set the outer and/or inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution upstream of the patterning device (in a pupil of the radiation system).
Fabrication of an integrated circuit pattern involves the control of space tolerances between features of the pattern, as well as control of feature dimension tolerances. In particular the control of tolerances of the smallest dimensions (such as for example the size of contacts or the width of lines or of spaces between two lines of a dense line space pattern) permitted in the fabrication of the integrated circuit device is of importance. The size of these most critical dimensions is referred to as the critical dimension (“CD”). Features having such a critical dimension may, hereinafter, be referred to as CD-sized features.
A measurement of a cross sectional profile in resist (the “resist profile”) of a feature or of a plurality of features may be used to obtain a measured value of the printed CD or a set of measured values of printed CD. In the present context, the printed CD refers to the dimension of a feature as obtained after post-exposure processing of an exposed resist layer.
With conventional projection lithographic techniques, an occurrence of a variance in printed CD may limit the process latitude or process window (i.e., the available depth of focus in combination with the allowed amount of residual error in the dose of exposure of irradiated target portions for a given tolerance on CD). The variance of printed CD arises because features of the patterning device having the same nominal critical dimensions may print differently depending on, for example, an amount of defocus (out of a plane of best focus) of the part of the target portion where the feature is imaged, due to, for example, substrate topography, image curvature or substrate unflatness.
The effect of focus on CD with a projection lithography printing process is a significant part in understanding and controlling the lithographic process. A change in focus not only alters the resist profile of a feature, but also increases the sensitivity of the resulting printed CD to other processing errors. For example, residual exposure-dose variations during a full substrate exposure may occur due to scan speed variations in a scanner apparatus. Since the effect of focus depends on exposure dose, a conventional method to judge the response of printed CD to focus and dose deviations is to execute a number of exposures of a test pattern including CD-sized features on a test substrate, whereby the different exposures are run at corresponding different combinations {E,F} of lithographic apparatus exposure-dose setting E and substrate focus-position setting F.
After completion of the different exposures, the test substrate is processed (including, for example a post-exposure bake step and a resist development step) and measurements of the printed CD can be done for each combination {E,F} of exposure dose and focus. The obtained measurement data representing a response of printed CD to exposure dose settings and focus settings of the lithographic apparatus can be visualized graphically. A response of printed CD to exposure dose setting and focus setting is, hereinafter, denoted by a function CD(E,F). Data describing such a dependency CD(E,F) of printed CD on exposure dose setting and focus setting are generally represented by a plot of printed CD (along a vertical axis) versus focus setting F (along a horizontal axis), for a constant exposure dose E. The corresponding curve or plot is referred to as a Bossung curve or plot.
From a series of Bossung plots with a corresponding series of exposure doses as parameter, important metrics for characterization of the lithographic process, when run on the lithographic apparatus, may be derived. Such metrics are, for example, the depth of focus (“DOF”) and the process window. Further, by including both dense and isolated CD-sized features in the test pattern, a measure for iso-dense bias may be obtained. Iso-dense bias refers to a difference in printed CD between two similar features such as lines arranged at two respective, different pitches.
Generally, a patterning device pattern is designed in such a way that differences in dimensions of printed isolated features and printed dense features are minimized to some degree, by applying a size bias to certain features. Applying, to the patterning device pattern, a size bias to certain features such as lines is referred to as feature-biasing and, in the case of lines, as line-biasing. The actual pitch dependency of printed CD depends, however, on the specific properties of the lithographic apparatus, such as for example projection system optical wave aberrations and settings of the apparatus such as the focus and exposure dose settings. Therefore, even in the presence of feature bias, a residual iso-dense bias may be present.
In view of the trend in the field of lithography to provide increasing numbers of features per area on the substrate, CD tolerance budgets are decreasing. Consequently a method of control of CD variations and iso-dense bias should be improved.
Conventionally, a response CD(E,F) of printed CD to changes CHE and CHF of respective preselected exposure dose and focus settings E0 and F0 is modeled as a power series in the changes CHE and CHF. In such a model the response CD(E,F) is given by
                                          CD            ⁡                          (                              E                ,                F                            )                                =                                    ∑                              i                ,                j                                            I                ,                J                                      ⁢                                          C                                  a                  ;                  ij                                            ⁢                              CH                E                i                            ⁢                              CH                F                j                                                    ⁢                                  ⁢        where                            (        1        )                                                      CH            E                    =                      E            -                          E              0                                      ⁢                                  ⁢                              CH            F                    =                      F            -                          F              0                                                          (        2        )            and where Ca;ij are model parameters. The powers i and j run from zero up to respective preselected values I and J.
It should be appreciated that F0 may for example be a first estimate of a best focus position BF of the substrate along the optical axis of the projection system. Similarly, the exposure dose E0 may be a first estimate of the best exposure dose needed to print a CD-sized feature at its nominal size. In accordance with Equation (1) a model of printed CD as a function of exposure dose and focus position is defined by a set of model parameters Ca;ij, the set being denoted as S {Ca;ij}.
A known method to control printed CD comprises utilizing exposure energy E and focus setting F as settable variables to affect CD. For example an effect of focus drift may be compensated by applying a focus offset to the lithographic apparatus. These techniques use models as described above in a control algorithm that relates exposure dose E and focus F to printed critical dimension. For example, an explicitly known model is the model with the set of model parameters S{Ca;00, Ca;10, all other Ca;ij=0}.
Another known model includes an expansion in powers of (1−E0/E)i, instead of CHei. See, for example, U.S. Pat. No. 6,643,596.
A known method includes a fitting of the model parameters to measured data of printed CD. The fitting involves reduction of the differences between the modeled data and the measured data for which various techniques and algorithms are available. For example, a least squares fitting can be used. The resulting “fitted” model parameters are stored and used by the control algorithm to calculate setting changes to be applied.
However, the effectiveness of the control of CD using a fitted CD response model significantly depends on the reliability of the model and the accuracy of the measurement data.